Facebook CEO Mark Zuckerberg is an "emperor for life" and therefore it will be hard to remove him from office, Yale management expert Jeffrey Sonnenfeld told CNBC on Tuesday.

"He's surely not going to voluntarily step down," Sonnenfeld said on "Closing Bell."

"He's not accountable to anybody," he added, noting that Zuckerberg controls about 60 percent of the stock.

Facebook shares closed lower for the second day on Tuesday in the wake of the privacy scandal.

Cambridge Analytica, which worked on Facebook ads for the Trump campaign, is accused of improperly gaining access to 50 million profiles before the 2016 election. Cambridge Analytica has called the allegations "false" and on Tuesday the board suspended CEO Alexander Nix. Facebook said it was deceived and vowed to vigorously enforce its policies to protect people's information.

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Facebook founder and CEO Mark Zuckerberg received an Honorary Doctor of Laws Degree from Harvard University at its 2017 366th Commencement Exercises on May 25, 2017 in Cambridge, Massachusetts.

"They're hiding. They're throwing up lawyers," he said. "They should show some accountability."

In a statement on Tuesday, Facebook said, "Mark, Sheryl and their teams are working around the clock to get all the facts and take the appropriate action moving forward, because they understand the seriousness of this issue. The entire company is outraged we were deceived."

As for who should run the social media giant, Sonnenfeld pointed to two possibilities currently sitting on the company's board. One is former American Express CEO Kenneth Chenault, and the other is Erskine Bowles, former chief of staff to President Bill Clinton and ex-Morgan Stanley lead director.

However, tech investor Jason Calacanis thinks Sandberg should step into the CEO role, telling "Closing Bell" on Monday that Zuckerberg has done a "horrible, horrible" job of handling the crisis.

Sandberg is a "better communicator" and a "tremendous leader," Calacanis said. "She's better at understanding how to manage these issues."

Facebook did not immediately respond to a request for comment on Sonnenfeld's remarks.